Funkcje pełnione w IF UMCS:

Abstract: The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ayon-Beato and Garcia and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration.

Abstract: Constructed within the framework of the Schwinger-DeWitt method, the renormalized stress-energy tensor of the quantized massive scalar, spinor and vector fields in a general spherically-symmetric and static spacetime is employed as a source term of the Einstein field equations. The semiclassical solutions describing the electrically charged black holes are obtained and their properties are studied. Special emphasis is put on the semiclassical extremal configurations: it is shown that the near-horizon geometry, when expanded into a whole manifold, is described by the Bertotti-Robinson line element.

Abstract: Building on general formulas obtained from the approximate renormalized effective action, the approximate stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling in the spacetime of a charged black hole that is the solution of the coupled equations of nonlinear electrodynamics and general relativity is constructed and analyzed. It is shown that, in a few limiting cases, the analytical expressions relating the obtained tensor to the general renormalized stress-energy tensor evaluated in the geometry of the Reissner-Nordstrom black hole can be derived. A detailed numerical analysis with special emphasis put on minimal coupling is presented, and the results are compared with those obtained earlier for a conformally coupled field. Some novel features of the renormalized stress-energy tensor are discussed.

Abstract: The analysis of binding energies of the sd shell nuclei appeared to be a new, interesting application of the supersymmetric model. After fitting the model parameters from masses and excited energy levels of well established nuclei it is possible to describe other exotic nuclei from the edge of a stability line, belonging to the same supermultiplet. We have applied such a procedure to the oxygen isotopes O-26,O-28. Th, method can be treated more generally for the construction of a supersymmetric mass formula for all of the sd shell nuclei. The results are quite satisfactory in comparison with experimental data and also with other theoretical predictions. It provides an additional argument for the approximate supersymmetry of the sd shell nuclei.

Abstract: We find a new class of time-dependent partial waves which are solutions of the time-dependent Schrodinger equation for three- dimensional harmonic oscillator. We also show the decomposition of coherent states of harmonic oscillator into these partial waves. This decomposition appears to be particularly convenient for a description of the dynamics of a wavepacket representing a particle with spin when the spin-orbit interaction is present in the Hamiltonian. An example of an evolution of a localized wavepacket into a torus and backwards, for particular initial conditions is analysed in analytical terms and shown with computer graphics.

Abstract: The supersymmetric model within the interacting boson model IBM4 with spin and isospin quantum numbers has been applied in our previous papers to the interpretation of energy levels and electromagnetic E2 transitions. The application of the model supersymmetric Hamiltonian to the binding energy calculations leads to the approximate mass formula with a relatively small number of parameters. The results when compared with experimental data are quite satisfactory, although not so good as extended shell model results. There is, however, another aim of this paper, namely to present an additional argument for the main assumption: the supersymmetry of the sd shell nuclei.

Abstract: This article discusses the properties of time evolution of wave packets in a few systems. Dynamics of wave packet motion for Rydberg atoms with the hierarchy of collapses and revivals is briefly reviewed. The main part of the paper focuses on the new mechanism of quantum recurrences in wave packet dynamics. This mechanism can occur in any physical system with strong enough spin-orbit interaction. We discuss here the spin-orbit pendulum effect that consists in different motions of subpackets with different spin fields and results in oscillations of a fraction of average angular momentum between spin and ordinary subspaces. The evolution of localized wave packets into toroidal objects and backwards (for other class of initial conditions) is also subject to discussion.